This study aims to understand the impact of composition on crystallization and chemical durability in alkali aluminoborosilicate based model nuclear waste glasses designed in the peralkaline, metaluminous and peraluminous regimes. The glasses have been thermally treated using the canister centerline cooling (CCC) schedule. The chemical durability of both parent and CCC-treated glasses has been assessed by product consistency test (PCT-B) for 120 days. The peraluminous glasses exhibit the highest dissolution rates, followed by peralkaline and metaluminous glasses. In general, increasing B2O3 content in glasses tends to suppress nepheline formation, thus, decreasing the negative impact of nepheline on durability of the final waste form. However, higher B2O3 content itself may result in detrimental impact on the durability of the final waste form. The thermal history has been shown to have a significant impact on the durability of the glasses.